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This paper describes an application of the Quantum Approximate Optimisation Algorithm (QAOA) to efficiently find approximate solutions for computational problems contained in the polynomially bounded NP optimisation complexity class (NPO…
Quantum walks are a promising framework that can be used to both understand and implement quantum information processing tasks. The quantum stochastic walk is a recently developed framework that combines the concept of a quantum walk with…
We propose a novel heuristic quantum algorithm for the Minimum Vertex Cover (MVC) problem based on continuous-time quantum walks (CTQWs). In this framework, the coherent propagation of a quantum walker over a graph encodes its structural…
The Maximum Matching problem has a quantum query complexity lower bound of $\Omega(n^{3/2})$ for graphs on $n$ vertices represented by an adjacency matrix. The current best quantum algorithm has the query complexity $O(n^{7/4})$, which is…
We solve an open problem by constructing quantum walks that not only detect but also find marked vertices in a graph. In the case when the marked set $M$ consists of a single vertex, the number of steps of the quantum walk is quadratically…
Providing an optimal path to a quantum annealing algorithm is key to finding good approximate solutions to computationally hard optimization problems. Reinforcement is one of the strategies that can be used to circumvent the exponentially…
Quantum annealing aims to exploit quantum mechanics to speed up the search for the solution to optimization problems. Most problems exhibit complete connectivity between the logical spin variables after they are mapped to the Ising spin…
Recently, several groups have investigated quantum analogues of random walk algorithms, both on a line and on a circle. It has been found that the quantum versions have markedly different features to the classical versions. Namely, the…
This paper introduces in detail a non-variational quantum algorithm designed to solve a wide range of combinatorial optimisation problems, including constrained problems and problems with non-binary variables. The algorithm returns optimal…
Quantum walk is a useful model to simulate complex quantum systems and to build quantum algorithms; in particular, to develop spatial search algorithms on graphs, which aim to find a marked vertex as quickly as possible. Quantum walks are…
We describe a method to simulate Hamiltonian evolution on a quantum computer by repeatedly using a superposition of steps of a quantum walk, then applying a correction to the weightings for the numbers of steps of the quantum walk. This…
Universal quantum computation can be realised using both continuous-time and discrete-time quantum walks. We present a version based on single particle discrete-time quantum walk to realize multi-qubit computation tasks. The scalability of…
It has been proved by Kempe that discrete quantum walks on the hypercube (HC) hit exponentially faster than the classical analog. The same was also observed numerically by Krovi and Brun for a slightly different property, namely, the…
Quantum annealing solves combinatorial optimization problems by finding the energetic ground states of an embedded Hamiltonian. However, quantum annealing dynamics under the embedded Hamiltonian may violate the principles of adiabatic…
We investigate how arbitrary number of entangled qubits affects properties of quantum walk. We consider variance, positions with non-zero probability density and entropy as criteria to determine the optimal number of entangled qubits in…
In recent times, hybrid-entanglement (HE) between a qubit and a coherent state has demonstrated superior performance in various quantum information processing tasks, particularly in quantum key distribution. Despite its theoretical…
Continuous-time quantum walks offer provable speedups for certain computational problems, yet translating these advantages to near-term hardware remains challenging. We present the first experimental demonstration of variational ans\"atze…
In this work, we present a new algorithm for generating quantum circuits that efficiently implement continuous time quantum walks on arbitrary simple sparse graphs. The algorithm, called matching decomposition, works by decomposing a…
With photonics, the quantum computational advantage has been demonstrated on the task of boson sampling. Next, developing quantum-enhanced approaches for practical problems becomes one of the top priorities for photonic systems. Quantum…
Quantum walks provide a versatile framework for probing the structural and dynamical properties of complex systems ranging from biological networks to synthetic materials. However, their realization on current noisy pre-fault-tolerant…